Algebra Examples

$- \frac{4}{7} (x - \frac{1}{4}) = \frac{3}{7}$

Step 1

Multiply both sides of the equation by $- \frac{7}{4}$ .

$- \frac{7}{4} (- \frac{4}{7} \cdot (x - \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- \frac{7}{4} (- \frac{4}{7} \cdot (x - \frac{1}{4}))$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$- \frac{7}{4} (- \frac{4}{7} x - \frac{4}{7} (- \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.2

Combine $x$ and $\frac{4}{7}$ .

$- \frac{7}{4} (- \frac{x \cdot 4}{7} - \frac{4}{7} (- \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.1.3.1

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- 4}{7} (- \frac{1}{4})) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.3.2

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- 4}{7} \cdot \frac{- 1}{4}) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.3.3

Factor $4$ out of $- 4$ .

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{4 (- 1)}{7} \cdot \frac{- 1}{4}) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.3.4

Cancel the common factor.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{4 \cdot - 1}{7} \cdot \frac{- 1}{4}) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.3.5

Rewrite the expression.

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- 1}{7} \cdot - 1) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.4

Combine $\frac{- 1}{7}$ and $- 1$ .

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{- - 1}{7}) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.1.5

Multiply $- 1$ by $- 1$ .

$- \frac{7}{4} (- \frac{x \cdot 4}{7} + \frac{1}{7}) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.2

Move $4$ to the left of $x$ .

$- \frac{7}{4} (- \frac{4 x}{7} + \frac{1}{7}) = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3

Simplify terms.

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Step 2.1.1.3.1

Apply the distributive property.

$- \frac{7}{4} (- \frac{4 x}{7}) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.2

Cancel the common factor of $7$ .

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Step 2.1.1.3.2.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$\frac{- 7}{4} (- \frac{4 x}{7}) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.2.2

Move the leading negative in $- \frac{4 x}{7}$ into the numerator.

$\frac{- 7}{4} \cdot \frac{- 4 x}{7} - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.2.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{4} \cdot \frac{- 4 x}{7} - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.2.4

Cancel the common factor.

$\frac{7 \cdot - 1}{4} \cdot \frac{- 4 x}{7} - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.2.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 x) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.3

Cancel the common factor of $4$ .

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Step 2.1.1.3.3.1

Factor $4$ out of $- 4 x$ .

$\frac{- 1}{4} (4 (- x)) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.3.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- x)) - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.3.3

Rewrite the expression.

$- - x - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.4

Multiply.

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Step 2.1.1.3.4.1

Multiply $- 1$ by $- 1$ .

$1 x - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.4.2

Multiply $x$ by $1$ .

$x - \frac{7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.5

Cancel the common factor of $7$ .

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Step 2.1.1.3.5.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$x + \frac{- 7}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.5.2

Factor $7$ out of $- 7$ .

$x + \frac{7 (- 1)}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.5.3

Cancel the common factor.

$x + \frac{7 \cdot - 1}{4} \cdot \frac{1}{7} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.5.4

Rewrite the expression.

$x + \frac{- 1}{4} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.1.1.3.6

Move the negative in front of the fraction.

$x - \frac{1}{4} = - \frac{7}{4} \cdot \frac{3}{7}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{7}{4} \cdot \frac{3}{7}$ .

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Step 2.2.1.1

Cancel the common factor of $7$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$x - \frac{1}{4} = \frac{- 7}{4} \cdot \frac{3}{7}$

Step 2.2.1.1.2

Factor $7$ out of $- 7$ .

$x - \frac{1}{4} = \frac{7 (- 1)}{4} \cdot \frac{3}{7}$

Step 2.2.1.1.3

Cancel the common factor.

$x - \frac{1}{4} = \frac{7 \cdot - 1}{4} \cdot \frac{3}{7}$

Step 2.2.1.1.4

Rewrite the expression.

$x - \frac{1}{4} = \frac{- 1}{4} \cdot 3$

Step 2.2.1.2

Combine $\frac{- 1}{4}$ and $3$ .

$x - \frac{1}{4} = \frac{- 1 \cdot 3}{4}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $- 1$ by $3$ .

$x - \frac{1}{4} = \frac{- 3}{4}$

Step 2.2.1.3.2

Move the negative in front of the fraction.

$x - \frac{1}{4} = - \frac{3}{4}$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $\frac{1}{4}$ to both sides of the equation.

$x = - \frac{3}{4} + \frac{1}{4}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{- 3 + 1}{4}$

Step 3.3

Add $- 3$ and $1$ .

$x = \frac{- 2}{4}$

Step 3.4

Cancel the common factor of $- 2$ and $4$ .

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Step 3.4.1

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{4}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 3.4.2.2

Cancel the common factor.

$x = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 3.4.2.3

Rewrite the expression.

$x = \frac{- 1}{2}$

Step 3.5

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$